Not really. As TCA Srinivasa-Raghavan pointed out, for TamBrahms curd rice is both necessary and sufficient1. However for Punjews aaloo parathas are only sufficient2, since they can be replaced by mooli parathas, gobi parathas, or makki di roti.

Put another way, you cannot be TamBrahm if you do not eat curd rice. You can be a Punjew even if you don’t eat aaloo parathas, as long as you eat makki di roti instead.

1: He was drawing an analogy to how Indian economists treat statistical jugglery.2: Provided they are two number aaloo parathas.